Optimal control of Bose–Einstein condensates in three dimensions

Abstract

Ultracold gases promise many applications in quantum metrology, simulation and computation. In this context, optimal control theory (OCT) provides a versatile framework for the efficient preparation of complex quantum states. However, due to the high computational cost, OCT of ultracold gases has so far mostly been applied to one-dimensional (1D) problems. Here, we realize computationally efficient OCT of the Gross-Pitaevskii equation to manipulate Bose-Einstein condensates in all three spatial dimensions. We study various realistic experimental applications where 1D simulations can only be applied approximately or not at all. Moreover, we provide a stringent mathematical footing for our scheme and carefully study the creation of elementary excitations and their minimization using multiple control parameters. The results are directly applicable to recent experiments and might thus be of immediate use in the ongoing effort to employ the properties of the quantum world for technological applications.

Fully efficient time-parallelized quantum optimal control algorithm

“…This subject has been extensively studied in the past few years [51,52,[54][55][56][57][58]. Following Ref.…”

Optimal control for feedback cooling in cavityless levitated optomechanics

“…We utilize optimal control theory to investigate both quadratic (parametric) and linear (electric) feedback (section 3). Optimal control theory has been applied to other experimental systems [41], including for manipulation of Bose-Einstein condensates to prepare complex quantum states [42], designing excitation pulses in NMR [43] and tailoring robustness in solid-state spin magnetometry [44]. Additionally, it has been proposed for mixed state squeezing in cavity optomechanics [45], feedback cooling and squeezing of levitated nanopshperes in cavities [46] and recently for feedback cooling in low frequency magnetic traps [27].…”

Coherent control of nonlinear mode transitions in Bose–Einstein condensates

“…The extent of the interference will be dictated by the magnitude of the couplings parameters β 12 and γ 12 . Additionally, according to (21), if the modulation of the scattering length is absent, then variation of θ plays no role in the dynamics.…”